New Washing Machine Vent Question

I recently installed a new drain and supply lines for a washing machine (see attached). I tapped into the main waste/soil stack just before it exits the house through the wall. The 18" standpipe is two feet away from the stack. I added a vent to be used with an AAV. My question: do I need the vent? I would prefer not to use the AAV if it's not required. I thought I read somewhere if the appliance is within 5 feet of the main stack, a vent is not necessary.